What is the integral from 0 to 2pi of (cos(θ))^2 ?

The integral from 0 to 2pi of (cos(θ))^2 is pi

Popular >

integral from 0 to 2pi of (cos(θ))^2

\int_{0}^{2 π} (cos (θ))^{2} d θ

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{2 π} (cos (θ))^{2} d θ

Simplify

= \int_{0}^{2 π} cos^{2} (θ) d θ

Rewrite using trig identities

= \int_{0}^{2 π} \frac{1 + cos ( 2 θ )}{2} d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{2 π} 1 + cos (2 θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{2 π} 1 d θ + \int_{0}^{2 π} cos (2 θ) d θ)

\int_{0}^{2 π} 1 d θ = 2 π

\int_{0}^{2 π} cos (2 θ) d θ = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\int_{0}^{1} 4 e^{x} d x

\int_{12}^{x} \frac{1}{t} d t

\int_{0}^{1} 4 x (x^{2} + 2)^{3} d x

\int_{- 1}^{0} 6 x^{2} (2 x^{3} + 4)^{2} d x

\int_{3}^{4} x ln (x) d x

What is the integral from 0 to 2pi of (cos(θ))^2 ?
The integral from 0 to 2pi of (cos(θ))^2 is pi